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The study of the spectrum of the Laplace operator has produced an extensive literature. (See [Cha] and the references therein.) Of special interest to recent applications has been the behavior of spec...
This paper studies Adaptive Finite Element Methods (AFEMs), based on piecewise liear elements and newest vertex bisection, for solving second order elliptic equations with piecewise constant coeʂ...
We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric second order linear elliptic operators. The method is formulated on nonconforming meshes made of simplices or q...
We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A − ∇div in H(div,Ω). For A being a variab...
Dispersing billiards with cusps are deterministic dnamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic paterns.
The Hausdorff distance between a compact convex set K CRd and random sets K c lRd iS studied. Basic inequalities are derived for the case of K being a convex subset of K. If applied to special seq...
On quantitative convergence to quasi-stationarity。
Making use of the Whittaker-Shannon interp olation formula w ith shifted sampling p oints, we prop ose in this pap e r a well-p osed semi-discretization of the stationary Wigner equation with inflow B...
In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive op...
The molecule solution of an extended discrete Lotka-Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this...
In an earlier paper, we presented an iterative algorithm for reconstructing a three dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy fun...
In this paper, we present a novel L2-gradient flow based semi-implicit finite element method for solving a variational model of image reconstruction under various data scenarios, especially for the ...
We consider the convergence theory of local multigrid methods for H1()-elliptic and H(curl,)-elliptic variational problems on bounded Lipschitz domains. In the context of lowest order conforming fin...
We propose a condition under which the heterogeneous multiscale 痭ite element method converges for elliptic problem with nonsmooth coe眂ients, and obtain the optimal convergence rate for elliptic prob...

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